Dabrafenib and Trametinib in People With BRAF V600E Mutation Positive Lesions in Erdheim Chester Disease

* INCLUSION CRITERIA: * All patients will be previously or simultaneously enrolled in the natural history ECD protocol #11-HG-0207, Clinical and Basic Investigations into Erdheim Chester disease . Eligible patients must have been diagnosed with Erdheim Chester disease, confirmed by pathological evaluation of the affected tissue with adequate staining. Affected tissue must harbor the BRAF V600E or V600K mutation. * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as greater than or equal to 20 mm with conventional techniques or as greater than or equal to 10 mm with spiral CT scan, MRI, or calipers by clinical exam. * Patients must have BRAFV600E or BRAFV600K mutations, identified by an FDAapproved test at a CLIAcertified lab. If test at CLIAcertified lab used a nonFDA approved method, information about the assay must be provided. (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test). * Prior treatment, involving interferon, anakinra, imatinib, steroids, chemotherapy with, but not limited to cladribine, vinblastine, 6-mercaptopurine and etoposide, or other medications used empirically for the treatment of ECD, will be acceptable. These therapies should have been completed and discontinued 4 weeks or more prior to enrollment in this study. * Age greater than or equal to18 years. Because no dosing or adverse event data are currently available on the use of dabrafenib in combination with trametinib in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (Karnofsky greater than or equal to 70%). Exception will be made for patients with ECOG performance status less than or equal to 3 and Karnofsky performance scale greater than or equal to 50%, who require the use of wheelchairs, walkers or canes as well as assistance with daily routines secondary to disabilities caused by ECD cerebellar or brain disease that has been stable for greater than or equal to 3 months. * Life expectancy of greater than 3 months. * Able to swallow and retain oral medication and must not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels. * Patients must have normal organ and marrow function as defined below: * Absolute neutrophil count (ANC) greater than or equal to1.2x10(9)/L * Hemoglobin greater than or equal to 9 g/dL * Platelets greater than or equal to100x10(9)/L * Albumin greater than or equal to2.5 g/dL * Serum bilirubin less than or equal to1.5x institutional upper limit of normal (ULN) except subjects with known Gilbert s syndrome * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to2.5x institutional ULN * Serum creatinine less than or equal to1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault formula) greater than or equal to 50 mL/min * Prothrombin time (PT)/International normalized ratio (INR) and partial thromboplastin time (PTT) less than or equal to1.3x institutional ULN; subjects receiving anticoagulation treatment may be allowed to participate with INR established within the therapeutic range prior to randomization. * Left ventricular ejection fraction greater than or equal to institutional lower limit of normal (LLN) by ECHO * Women of childbearing potential must have a negative serum pregnancy test within 14 days prior to registration or randomization. * Pregnancy and breast feeding. The effects of dabrafenib and trametinib on the developing human fetus are unknown. For this reason women of child-bearing potential must agree to use adequate contraception (barrier method of birth control, or abstinence; hormonal contraception is not allowed due to drug-drug interactions which can render hormonal contraceptives ineffective) for the duration of study participation, and for at least 2 weeks after treatment with dabrafenib or for 4 months after dabrafenib in combination with trametinib. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. Based on studies in animals, it is also known that dabrafenib may cause damage to the tissue that makes sperm. This may cause sperm to be abnormal in shape and size and could lead to infertility, which may be irreversible. Safety and efficacy of the combination of dabrafenib and trametinib in pediatric populations have not been investigated. Dabrafenib or trametinib-dabrafenib combination should not be administered to pediatric populations outside clinical trials. * Therapeutic level dosing of warfarin can be used with close monitoring of PT/INR by the site. Exposure may be decreased due to enzyme induction when on treatment, thus warfarin dosing may need to be adjusted based upon PT/INR. Consequently, when discontinuing dabrafenib, warfarin exposure may be increased and thus close monitoring via PT/INR and warfarin dose adjustments must be made as clinically appropriate. Prophylactic low dose warfarin may be given to maintain central catheter patency. * Ability to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA * Inability to provide informed consent. * Prior systemic anti-cancer therapy (chemotherapy with delayed toxicity, extensive radiation therapy, immunotherapy, biologic therapy, or vaccine therapy) within the last 3 weeks; chemotherapy regimens without delayed toxicity within the last 2 weeks preceding the first dose of study treatment. * Use of other investigational drugs within 28 days (or five half-lives, whichever is shorter; with a minimum of 14 days from the last dose) preceding the first dose of study treatment and during the study. Patients that have used other BRAF or MEK inhibitor are excluded. * Current use of a prohibited medication. Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A or CYP2C8 are ineligible. Current use of, or intended ongoing treatment with: herbal remedies (e.g., St. John s wort), or strong inhibitors or inducers of P-glycoprotein (Pgp) or breast cancer resistance protein 1 (Bcrp1) should also be excluded. * Unresolved toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.0 (NCI CTCAE v4.0) grade 2 or higher from previous anti-cancer therapy, except alopecia. * Human Immunodeficiency Virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with dabrafenib. * A history of Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) infection (with the exception of cleared HBV and HCV infection, which will be allowed). * Presence of malignancy other than the study indication under this trial within 3 years of study enrollment. * Patients with history of RAS mutation-positive tumors are not eligible regardless of interval from the current study. Note: RAS testing and absence of RAS mutation are required for eligibility. * Leptomeningeal or brain metastases or metastases causing spinal cord compression that are symptomatic or untreated or not stable for greater than or equal to 3 months (must be documented by imaging) or requiring corticosteroids. Subjects on a stable dose of corticosteroids \>1 month or who have been off of corticosteroids for at least 2 weeks can be enrolled with approval of the CTEP medical monitor. Subjects must also be off of enzyme-inducing anticonvulsants for \>4 weeks. * History or evidence of cardiovascular risks, except stable ECD cardiac lesion, including any of the following: QT interval corrected for heart rate using the Bazett s formula QTcB greater than or equal to 480 msec. History of acute coronary syndromes (including myocardial infarction or unstable angina), coronary angioplasty, or stenting within the past 24 weeks prior to randomization. History or evidence of current Class II, III, or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system. Intra-cardiac defibrillators. Abnormal cardiac valve morphology (greater than or equal to grade 2) documented by ECHO; (subjects with grade 1 abnormalities \[i.e., mild regurgitation/stenosis\] can be entered on study). Subjects with moderate valvular thickening should not be entered on study. History or evidence of current clinically significant uncontrolled cardiac arrhythmias; clarification: Subjects with atrial fibrillation controlled for \>30 days prior to dosing are eligible. Treatment refractory hypertension defined as a blood pressure of systolic \>140 mmHg and/or diastolic \> 90 mm Hg which cannot be controlled by anti-hypertensive therapy * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO). * Any serious or unstable pre-existing medical conditions (aside from malignancy exceptions specified above), psychiatric disorders, or other conditions that could interfere with the subject s safety, obtaining informed consent, or compliance with study procedures. * Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with dabrafenib/trametinib, breastfeeding should be discontinued prior to treatment with dabrafenib/trametinib. These potential risks may also apply to other agents used in this study. * History of retinal vein occlusion (RVO). * Interstitial lung disease or pneumonitis not secondary to ECD. * Central serous retinopathy (CSR) including presence of predisposing factors to RVO or CSR (e.g., uncontrolled glaucoma or ocular hypertension, uncontrolled diabetes mellitus, or a history of hyperviscosity or hypercoagulability syndromes); or visible pathology (e.g., evidence of optic disc cupping, evidence of new visual field defects on automated perimetry, or intraocular pressure \>21 mmHg as measured by tonography) as assessed by ophthalmic examination. * Inability to travel to the NIH Clinical Center. * Patients with wild type BRAF gene molecular results on ECD affected tissue. * Patients with confirmed diagnosis of ECD that are asymptomatic and with no visceral involvement are not eligible for this trial (Patients with no target lesions as per RECIST 1.1 criteria.